Shelf Load & Sag Calculator

ANA›Life Services Authority›National Calculator Authority›Shelf Load & Sag Calculator

.calc-container { max-width: 640px; margin: 2rem 0; padding: 1.5rem; background: #fff; border: 1px solid #ddd; border-radius: 8px; box-shadow: 0 1px 3px rgba(0,0,0,0.06); font-family: system-ui, -apple-system, sans-serif; } .calc-container h3 { font-family: Georgia, serif; font-size: 1.15rem; color: #1a1a1a; margin-bottom: 1rem; padding-bottom: 0.5rem; border-bottom: 2px solid var(--ac, #3d5a80); } .calc-row { display: flex; align-items: center; gap: 0.75rem; margin-bottom: 0.75rem; flex-wrap: wrap; } .calc-row label { min-width: 160px; font-size: 0.9rem; color: #333; font-weight: 500; } .calc-row input[type="number"], .calc-row select { flex: 1; min-width: 120px; max-width: 200px; padding: 0.5rem 0.6rem; border: 1px solid #ccc; border-radius: 4px; font-size: 0.9rem; font-family: system-ui, sans-serif; color: #1a1a1a; background: #fafaf8; } .calc-row input:focus, .calc-row select:focus { outline: none; border-color: var(--ac, #3d5a80); box-shadow: 0 0 0 2px rgba(26,74,138,0.12); } .calc-row .unit { font-size: 0.82rem; color: #888; min-width: 30px; } .calc-btn { display: inline-block; margin-top: 0.5rem; padding: 0.55rem 1.5rem; background: var(--ac, #3d5a80); color: #fff; border: none; border-radius: 4px; font-size: 0.9rem; font-weight: 600; cursor: pointer; font-family: system-ui, sans-serif; } .calc-btn:hover { opacity: 0.9; } .calc-result { margin-top: 1.25rem; padding: 1rem 1.25rem; background: #f0f6fc; border-left: 3px solid var(--ac, #3d5a80); border-radius: 0 6px 6px 0; display: none; } .calc-result.visible { display: block; } .calc-result-label { font-size: 0.78rem; text-transform: uppercase; letter-spacing: 0.06em; color: #666; margin-bottom: 0.25rem; } .calc-result-value { font-size: 1.6rem; font-weight: 700; color: var(--ac, #3d5a80); } .calc-result-detail { font-size: 0.85rem; color: #555; margin-top: 0.5rem; line-height: 1.5; } .calc-note { margin-top: 1rem; font-size: 0.8rem; color: #888; font-style: italic; } .calc-grid { display: grid; grid-template-columns: 1fr 1fr; gap: 0.75rem; margin-top: 0.75rem; } .calc-grid-item { padding: 0.6rem 0.8rem; background: #f8f9fa; border-radius: 4px; border: 1px solid #eee; } .calc-grid-item .label { font-size: 0.75rem; color: #888; text-transform: uppercase; letter-spacing: 0.04em; } .calc-grid-item .value { font-size: 1.1rem; font-weight: 600; color: #1a1a1a; } @media (max-width: 720px) { .calc-row { flex-direction: column; align-items: flex-start; gap: 0.3rem; } .calc-row label { min-width: auto; } .calc-row input[type="number"], .calc-row select { max-width: 100%; width: 100%; } .calc-grid { grid-template-columns: 1fr; } } .calc-chart { margin: 1rem 0; text-align: center; } .calc-chart svg { max-width: 100%; height: auto; } .calc-chart-legend { display: flex; flex-wrap: wrap; justify-content: center; gap: 0.6rem 1.2rem; margin-top: 0.6rem; font-size: 0.8rem; color: #555; } .calc-chart-legend span { display: inline-flex; align-items: center; gap: 0.3rem; } .calc-chart-legend i { display: inline-block; width: 10px; height: 10px; border-radius: 2px; font-style: normal; } .calc-related { max-width: 640px; margin: 2rem 0 1rem; padding: 1.25rem 1.5rem; background: #f8f9fa; border: 1px solid #e8e8e8; border-radius: 8px; } .calc-related h3 { font-family: Georgia, serif; font-size: 1rem; color: #1a1a1a; margin: 0 0 0.75rem; padding-bottom: 0.4rem; border-bottom: 2px solid var(--ac, #3d5a80); } .calc-related-list { list-style: none; padding: 0; margin: 0 0 0.75rem; display: grid; grid-template-columns: 1fr 1fr; gap: 0.4rem 1.5rem; } .calc-related-list li a { font-size: 0.88rem; color: var(--ac, #3d5a80); text-decoration: none; } .calc-related-list li a:hover { text-decoration: underline; } .calc-browse-all { margin: 0.5rem 0 0; font-size: 0.9rem; font-weight: 600; } .calc-browse-all a { color: var(--ac, #3d5a80); text-decoration: none; } .calc-browse-all a:hover { text-decoration: underline; } @media (max-width: 720px) { .calc-related-list { grid-template-columns: 1fr; } }

Shelf Load & Sag Calculator

Calculate the maximum mid-span deflection (sag) and bending stress of a shelf treated as a simply supported beam under a uniform distributed load.

Shelf Span, L (mm)

mm

Shelf Width / Depth, b (mm)

mm

Shelf Thickness, h (mm)

mm

Total Load on Shelf, W (kg)

kg

Elastic Modulus, E (MPa)

Steel – 200,000 MPa Aluminium – 70,000 MPa Plywood / Hardwood – 12,000 MPa MDF / Particleboard – 3,500 MPa Custom…

Custom E (MPa)

MPa

Calculate

(function(){ / Show/hide custom E field / document.getElementById('she-emod').addEventListener('change', function(){ document.getElementById('she-custom-e-row').style.display = this.value === 'custom' ? 'flex' : 'none'; });

window.sheCalc = function(){ const resultDiv = document.getElementById('she-result');

/ --- gather inputs --- /
const L = parseFloat(document.getElementById('she-length').value);
const b = parseFloat(document.getElementById('she-width').value);
const h = parseFloat(document.getElementById('she-thickness').value);
const Wkg = parseFloat(document.getElementById('she-load').value);
const eSelect = document.getElementById('she-emod').value;
const E = eSelect === 'custom'
? parseFloat(document.getElementById('she-custom-e').value)
parseFloat(eSelect);

/ --- validation --- / const errors = []; if (isNaN(L) || L = L) errors.push("Thickness h must be less than span L.");

if (errors.length > 0){ resultDiv.innerHTML = '' + errors.map(e => '').join('') + ''; return; }

/ --- core calculations --- / const g = 9.81; // m/s² const W_N = Wkg * g; // total load in Newtons

/ Second moment of area: rectangular cross-section I = b·h³ / 12 (mm⁴) / const I = (b * Math.pow(h, 3)) / 12;

/ Uniform distributed load intensity w = W / L (N/mm) / const w = W_N / L;

/ Maximum deflection (mid-span) for simply supported beam, UDL: δ_max = 5·w·L⁴ / (384·E·I) (mm) / const delta_max = (5 * w * Math.pow(L, 4)) / (384 * E * I);

/ Sag as a fraction of span / const sagRatio = delta_max / L;

/ Maximum bending moment (mid-span): M_max = w·L² / 8 (N·mm) / const M_max = (w * Math.pow(L, 2)) / 8;

/ Maximum bending stress (at extreme fibre): σ_max = M_max · (h/2) / I (MPa = N/mm²) / const sigma_max = (M_max * (h / 2)) / I;

/ Maximum shear force (at supports): V_max = W / 2 (N) / const V_max = W_N / 2;

/ --- serviceability assessment --- / / Common guideline: δ ≤ L/360 for shelving / const limit_360 = L / 360; const limit_200 = L / 200; let sagStatus, sagColor; if (delta_max ParameterValue Second Moment of Area, I${I.toLocaleString(undefined,{maximumFractionDigits:1})} mm⁴ UDL intensity, w${w.toFixed(4)} N/mm Max Bending Moment, Mmax${(M_max/1000).toFixed(2)} N·m Max Shear Force, Vmax${V_max.toFixed(1)} N Max Bending Stress, σmax${sigma_max.toFixed(2)} MPa Max Deflection (Sag), δmax ${delta_max.toFixed(2)} mm Sag as Fraction of SpanL / ${(1/sagRatio).toFixed(0)} L/360 Limit${limit_360.toFixed(2)} mm L/200 Limit${limit_200.toFixed(2)} mm Serviceability ${sagStatus} `; }; })();

#### Formulas Used

Second Moment of Area (rectangular section): I = b · h³ / 12

UDL intensity: w = W / L    (W in Newtons, L in mm)

Maximum deflection – simply supported beam, UDL (mid-span): δmax = 5 · w · L⁴ / (384 · E · I)

Maximum bending moment (mid-span): Mmax = w · L² / 8

Maximum bending stress (extreme fibre): σmax = Mmax · (h/2) / I

Maximum shear force (at supports): Vmax = W / 2

#### Assumptions & References

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References

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